Cumulative Frequency

Worksheets Answers

Worksheet 1: Programme Questions

1. 1 to 15
2. 56
3. Vertical
4. (n+1)/2
5. Lower and upper quartiles
6. The London College of Fashion
7. Inside leg
8. 60cm
9. The box
10. The 16 to 30 group, by approximately 2cm

Worksheet 2: Tick or Trash

Question 1

Student B is correct. Student A has read the scale on the cumulative frequency axis wrongly.

Question 2

Student B is correct. Student A has plotted at the midpoint of class intervals.

Worksheet 3: Exam Practice Questions (Edexcel)

This is a selection of past exam questions from Edexcel, targeted at the middle ability range. You can use the sequence as it stands or select individual questions to suit your needs.

Below is the mark scheme for each question, which may help you to see how marks are allocated and what the examiner is especially looking for. The mark schemes use the following abbreviations:

oe	or equivalent
cao	correct answer only
ft	follow-through marks
dep	dependent
indep	independent
M	method marks
A	accuracy marks
B	benefit-of-doubt mark
SC	special case

Question 1

(a) 41 x 2.5 + 26 x 7.5 + ...
102.5 + 195 + 250 + 175 + 67.5
'790' ÷ 100 = 7.9 years

(b) 41, 67, 87, 97, 100

(c) Points correct. Curve or straight line segments

(d) 75 or 75 ¾ years indicated
11.5 (curve) 12 (lines)

Notes:
(a) M1 for fx using at least 3 consistent values in the intervals,
including both ends
M1 (dep) for use of correct mid-interval values
M1 for Sfx and division by 100 (dep on first M1)
A1 cao
(b) B1
(c) B1 for 4 or 5 points correctly plotted at ends of intervals (± half a square),
ft from sensible table in (b)
B1 ft from their points if previous B1 scored, or if B1 scored in (b) and points plotted consistently
(d) M1
A1 ft from graph (± half a square) if B2 or B1 in (c)

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Question 2

(a) 25 + 1 th = 13th number
2
Answer 16 to 20
(b) 3 x 1, 8 x 2, 13 x 5, 18 x 7, 23 x 8, 28 x 2, = 3, 16, 65, 126, 184, 56
450 ÷ 25 = 18 points
(c) 1, 3, 8, 15, 23, 25
(d) Graph drawn
(e) 18.5 points

Notes:
(a) M1 for identifying 13th number. Accept 12.5th
A1 cao for 16 to 20
(b) M1 for using values in the intervals (including both ends) consistently (at least 4 correct) x frequencies
M1 (dep) for adding fx values and ÷ 25
A1 cao for 18
(c) B2 all correct
(B1 if 5 or 4 correct or no more than one independent numerical error)
(d) B1 for axes drawn and labelled with words
B1 for points plotted with correctly ft cf at ends of intervals with a continuous scale (condone one plotting error)
B1 ft their points for smooth curve or line segments
(last two B marks dependent on at least B1 in part (c))
(e) B1 for using 13 or 12.5 and ft for an answer from graph ±0.5 (dep on at least B1 in part (c))
SC: If use fx values instead of f for cf table give 0 for (c), but in (d) and
(e) ignore the deps, and in (e) allow use of half the candidate's largest cf.

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Question 3

(a) 6, 23, 45, 90, 116, 135, 144, 150
(b) Cumulative frequency diagram drawn: ignore line between first point and the origin
(c) 60% of 150 = 90
150 - 90 = 60
Pass mark about 42-45 marks

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Question 4

(a) Mid-point Total
162.5 1137.5
167.5 1005
172.5 345
177.5 1775
182.5 912.5
Total 5175
Mean = 5175 ÷ 30 = 172.5cm
(b) 7, 13, 15, 25, 30
(c) Median = 175
Interquartile range = 17

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Question 5

(a) Plot points, joined with smooth curve/line
(b) Segments 240 - 170 = 70
(c) 10% = 12 houses. Read off where cf = 120 - 12 = 108;
floor area = 275m²